1,721,007 research outputs found
The Hardy–Littlewood lemma and the estimate for the d-barNeumann problem in a general norm
No full textWe prove a generalized Hardy-Littlewood lemma on a non-smooth domain in the "f-norm" and give an application to a corresponding estimate for the partial derivative-Neumann problem by means of suitable weights. (c) 2013 Elsevier Inc. All rights reserved
Testing families of analytic discs in the unit ball of C2
Full text linkLet a, b, c ? C-2 be three non-collinear points such that their mutual joining complex lines do not intersect the unit ball B-2 and such that the line through a and b is tangent to B-2. Then the set of lines concurrent to a, b or c is a testing family for continuous functions on S-3. This improves a result by the authors and solves a case left open in the literature as described by Globevnik
Characterization of continuous homomorphisms on entire slice monogenic functions
No full textThis paper is inspired by a class of infinite order differential operators arising in quantum mechanics. They turned out to be an important tool in the investigation of evolution of superoscillations with respect to quantum fields equations. Infinite order differential operators act naturally on spaces of holomorphic functions or on hyperfunctions. Recently, infinite order differential operators have been considered and characterized on the spaces of entire monogenic functions, i.e. functions that are in the kernel of the Dirac operators. The focus of this paper is the characterization of infinite order differential operators that act continuously on a different class of hyperholomorphic functions, called slice hyperholomorphic functions with values in a Clifford algebra or also slice monogenic functions. This function theory has a very reach associated spectral theory and both the function theory and the operator theory in this setting are subjected to intensive investigations. Here we introduce the concept of proximate order and establish some fundamental properties of entire slice monogenic functions that are crucial for the characterization of infinite order differential operators acting on entire slice monogenic functions
Existence and Interior Regularity Theorems for ∂ ̄ on Q-Convex Domains
No full textWe establish for a q-convex domain Ω ⊂ Cn existence results in Lp,k-12(Ω,loc) and Cp,k-1∞(Ω) for the equation ∂ ̄ u= f, where f is a (p, k)-form on Ω of degree k≥ q such that ∂ ̄ f= 0
COMPACTNESS ESTIMATES FOR square(b) ON A CR MANIFOLD
No full textThis paper aims to state compactness estimates for the Kohn-Laplacian on an abstract CR manifold in full generality. The approach consists of a tangential basic estimate in the formulation given by the first author in his thesis, which refines former work by Nicoara. It has been proved by Raich that on a CR manifold of dimension 2n - 1 which is compact pseudoconvex of hypersurface type embedded in the complex Euclidean space and orientable, the property named "(CR - P-q)" for 1 <= q <= n-1/2, a generalization of the one introduced by Catlin, implies compactness estimates for the Kohn-Laplacian square(b) in any degree k satisfying q <= k <= n - 1 - q. The same result is stated by Straube without the assumption of orientability. We regain these results by a simplified method and extend the conclusions to CR manifolds which are not necessarily embedded nor orientable. In this general setting, we also prove compactness estimates in degree k = 0 and k = n - 1 under the assumption of (CR - P-1) and, when n=2, of closed range for partial derivative(b). For n >= 3, this refines former work by Raich and Straube and separately by Straube
Il diritto alle libere elezioni - Aspetti internazionalistici e loro applicazione nella Repubblica federale di Jugoslavia
No full textIl contributo si propone, nella sua prima parte (redatta da S. Pinton) di verificare l'oggetto del diritto a partecipare a libere elezioni previsto da vari strumenti internazionali; nella seconda parte (redatta da S. Forlati) di valutare l'applicabilità di tali strumenti (in particolare, del Patto sui diritti civili e politici del 1966) alla Repubblica federale di Iugoslavia
Uniform regularity in a wedge and regularity of traces of CR functions
No full textWe discuss in Sect. 1 the property of regularity at the boundary of separately holomorphic functions along families of discs and apply, in Sect. 2, to two situations. First, let W be a wedge of C n with C ω, generic edge ε: a holomorphic function f on W has always a generalized (hyperfunction) boundary value bv(f) on ε, and this coincides with the collection of the boundary values along the discs which have C ω transversal intersection with ε. Thus Sect. 1 can be applied and yields the uniform continuity at ε of f when bv(f) is (separately) continuous. When W is only smooth, an additional property, the temperateness of f at ε, characterizes the existence of boundary value bv(f) as a distribution on ε. If bv(f) is continuous, this operation is consistent with taking limits along discs (Theorem 2.8). By Sect. 1, this yields again the uniform continuity at ε of tempered holomorphic functions with continuous bv. This is the theorem by Rosay (Trans. Am. Math. Soc. 297(1):63-72, 1986), in whose original proof the method of "slicing" by discs is not used. As related literature we mention, among others, Sato et al. (Lecture Notes in Mathematics, vol. 287, pp. 265-529, Springer, Berlin, 1973), Komatsu (J. Fac. Sci., Univ. Tokyo Sect. IA, Math. 19:201-214, 1972), Hörmander (Grundlehren der mathematischen Wissenschaften, vol. 256, Springer-Verlag, Berlin, 1984), Cordaro and Treves (Annals of Mathematics Studies, vol. 136, Princeton University Press, Princeton, 1994), Baouendi et al. (Princeton Mathematical Series, Princeton University Press, Princeton, 1999) and Berhanu and Hounie (Math. Z. 255:161-175, 2007). © 2010 Mathematica Josephina, Inc
ON THE EKELAND-HOFER SYMPLECTIC CAPACITIES OF THE REAL BIDISC
Full text linkIn C-2 with the standard symplectic structure we consider the bidisc D-2 x D-2 constructed as the product of two open real discs of radius 1. We compute explicit values for the first, second and third Ekeland-Hofer symplectic capacity of D-2 x D-2. We discuss some applications to questions of symplectic rigidity
The Noncommutative Fractional Fourier Law in Bounded and Unbounded Domains
Full text linkUsing the spectral theory on the S-spectrum it is possible to define the fractional powers of a large class of vector operators. This possibility leads to new fractional diffusion and evolution problems that are of particular interest for nonhomogeneous materials where the Fourier law is not simply the negative gradient operator but it is a nonconstant coefficients differential operator of the form T=∑l=13elal(x)∂xl,x=(x1,x2,x3)∈Ω ̄,where, Ω can be either a bounded or an unbounded domain in R3 whose boundary ∂Ω is considered suitably regular, Ω ̄ is the closure of Ω and el, for l= 1 , 2 , 3 are the imaginary units of the quaternions H. The operators Tl:=al(x)∂xl, for l= 1 , 2 , 3 , are called the components of T and a1, a2, a3: Ω ̄ ⊂ R3→ R are the coefficients of T. In this paper we study the generation of the fractional powers of T, denoted by Pα(T) for α∈ (0 , 1) , when the operators Tl, for l= 1 , 2 , 3 do not commute among themselves. To define the fractional powers Pα(T) of T we have to consider the weak formulation of a suitable boundary value problem associated with the pseudo S-resolvent operator of T. In this paper we consider two different boundary conditions. If Ω is unbounded we consider Dirichlet boundary conditions. If Ω is bounded we consider the natural Robin-type boundary conditions associated with the generation of the fractional powers of T represented by the operator ∑l=13al2(x)nl(x)∂xl+a(x)I, for x∈ ∂Ω , where I is the identity operator, a: ∂Ω → R is a given function and n= (n1, n2, n3) is the outward unit normal vector to ∂Ω. The Robin-type boundary conditions associated with the generation of the fractional powers of T are, in general, different from the Robin boundary conditions associated to the heat diffusion problem which leads to operators of the type ∑l=13al(x)nl(x)∂xl+b(x)I, x∈ ∂Ω. For this reason we also discuss the conditions on the coefficients a1, a2, a3: Ω ̄ ⊂ R3→ R of T and on the coefficient b: ∂Ω → R so that the fractional powers of T are compatible with the physical Robin boundary conditions for the heat equations
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